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Comp."],"abstract":"<p>We present explicit constructions of orthogonal polynomials inside quadratic bodies of revolution, including cones, hyperboloids, and paraboloids. We also construct orthogonal polynomials on the surface of quadratic surfaces of revolution, generalizing spherical harmonics to the surface of a cone, hyperboloid, and paraboloid. We use this construction to develop cubature and fast approximation methods.<\/p>","DOI":"10.1090\/mcom\/3544","type":"journal-article","created":{"date-parts":[[2020,3,4]],"date-time":"2020-03-04T09:39:19Z","timestamp":1583314759000},"page":"2847-2865","source":"Crossref","is-referenced-by-count":18,"title":["Orthogonal polynomials in and on a quadratic surface of revolution"],"prefix":"10.1090","volume":"89","author":[{"given":"Sheehan","family":"Olver","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuan","family":"Xu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2020,6,5]]},"reference":[{"issue":"19","key":"1","first-page":"5","article-title":"A method of constructing orthogonal polynomials of two variables for a certain class of weight functions","volume":"20","author":"Agahanov, S. 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